Category Archives: History of science

Giants’ Shoulders #70 celebrates a birthday.

Hans Sloane is one of those figures in the history of science, who deserves to be much better known than he is. Although Sloane Square in London is named after him, giving name to one of the horrors of modern English culture, the Sloane Ranger, most people would be hard put to it to say who he was.

Sir Hans Sloane Gottfried Kneller

Sir Hans Sloane
Gottfried Kneller

An Irish physician who lived through the second half of the seventeenth century and the first half of the eighteenth, he was a central figure in the English scientific community that included Hooke, Wren, Halley, Flamsteed and Newton as well as many other less well known personages. He was secretary of the Royal Society when Newton became its president in 1704 and very much shared the power with the great Sir Isaac in that august body until he resigned in 1713, after a series of power struggles with other council members over the preceding years. He got his revenge however when he was elected president following Newton’s death in 1727, a post he retained until 1741.

He served three English monarchs, Anne, George I and George II, as royal physician and was appointed baronet for his services in 1716. He was also elected president of the Royal College of Physicians in 1719 a post he would hold for sixteen years. In 1722 he also became physician-general to the army.

From the modern point of view Sloan’s most important activity was that of collector. Scientific curiosity cabinets were very much en vogue in the Early Modern Period and Sloane collected scientific curiosities on an almost unbelievable scale. When he died, in 1753, he donated his monster collection to the nation on the condition that the government build a museum to house it. The government agreed and so the venerable British Museum was born. Later Sloane’s natural history collection was given a home of its own leading to the establishment of the Natural History Museum.

Like many of his contemporaries, and in particular the collectors, Sloane was a prolific letter writer and, as is befitting in this digital age, his correspondence has its own blog. To celebrate Sir Hans’ 354th birthday, on 16 April, Giants’ Shoulders #70, the history of science, medicine and technology blog carnival  will take place at The Sloane Letters Blog hosted by our favourite blogging beagle, Lisa Smith (@historybeagle). Submission for this special birthday edition of Giants’ Shoulders should be made either direct to the host or to me here at RM or to either of us on Twitter at the latest by 15 April.

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Filed under Giants' Shoulders, History of medicine, History of science

Did Edmond tells Robert to, “sling his hooke!”?

The circumstances surrounding the genesis and publication of Newton’s magnum opus, Philosophiæ Naturalis Principia Mathematica, and the priority dispute concerning the origins of the concept of universal gravity are amongst the best documented in the history of science. Two of the main protagonists wrote down their version of the story in a series of letters that they exchanged, as the whole nasty affair was taking place. Their explanations are of necessity biased and unfortunately we don’t have equivalent written evidence from the third protagonist Robert Hooke, although we do have the earlier exchange of letters between Hooke and Newton that led Hooke to making his claims to being the author of the idea. All of this is documented, analysed and discussed in detail by Richard S. Westfall in his authoritative biography of Newton, Never at Rest. Lisa Jardine sketches the whole sorry episode in the introduction to her Hooke biography The Curious Life of Robert Hooke: The Man Who Measured London. Beyond this there is a whole raft full of academic papers and monographs on Hooke, Newton, Halley, Principia and the Royal Society that discus the whole or various aspects of the story. Any first year history of science student should be able to write an accurate and informed essay or term paper on this important moment in the history of seventeenth-century scientific publishing. In fact it would make a very useful exercise for such students. The scriptwriters of Cosmos would however get a fat F for their efforts to present the story. Maybe they should have turned to one of those first year students for help?

Thanks to the services of a beautiful fairy princess I was finally able to watch the third episode of the much hyped American television series Cosmos and, as predicted by numerous commentators on Twitter, I was more than underwhelmed by the animation telling the story of the publication of Principia Mathematica and its significance in the history of science.

Our tale starts with an introductions to the hero of the day, Edmond Halley, an interesting choice of which I actually approve but the first error come up with the tale of the young Halley’s journey to St Helena to map the southern skies. We get told that this is the first such map. This is simply not true Dutch seamen had already started mapping the southern hemisphere at the end of the sixteenth-century. Halley’s government sponsored voyage was the English attempt to catch up. Having established Halley as a scientific hero we get presented with Robert Hooke who is to play the villain of the piece.

At the beginning we get a very positive portrait of Hooke outlining the very wide range of his scientific activities. Unfortunately this presentation is spoilt by a series of bad history of science blunders. Introducing Hooke’s microscopic investigations we get told that Hooke invented the compound microscope. Given that compound microscopes were in use twenty years before Hooke was born, I hardly think so. We then get told that Hooke improved the telescope. Whilst it is true that Hooke proposed several schemes to improve the telescope, some of them positively Heath-Robinson, none of them really proved practical and there are no real improvements to the telescope that can be laid at Hooke’s door. Next up we are informed that Hooke perfected the air pump. Hooke did indeed construct the air pump that he and Robert Boyle used for their experiments, their model was in fact ‘perfected’, although improved would be a better term as it was anything but perfect, by Denis Papin.

Moving on, we are introduced to the London coffee houses, without doubt centres of scientific communication in the late seventeenth- and early eighteenth-centuries. However Tyson claims them to be laboratories of democracy. Sorry but all I can say to this piece of hogwash is bullshit. We come to the coffee house because of a legendary conversation between Halley, Hooke and Christopher Wren that took place in one of them in January 1684, concerning the law of gravity. This conversation is indisputably a key moment in the history of science and that is the reason why it is featured in this episode of Cosmos. Given this one would expect that the scriptwriters would get the story right, however ones expectations would be dashed. According to Cosmos the three speculated as to whether there was a mathematical law governing celestial motion and then Newton, to whom I will come in a minute, produced the inverse squared law of gravity like a conjuror pulling his rabbit out of his hat. In fact all three participants were aware of speculations concerning an inverse squared law of gravity and Hooke claimed that he could deduce the motions of the heavens from it. Wren doubted this claim and offered a prize for the first to do so. Hooke persisted that he already had the solution but would first reveal it when the others had admitted defeat.

Cosmos has Halley, unable to solve the problem rushing off the Cambridge to ask Newton if he could solve it. In fact Halley being in Cambridge in August of the same year met Newton and in the course of their conversation asked Newton, “what he thought the Curve would be that would be described by the Planets supposing the force of attraction towards the Sun to be reciprocal to the square of their distance from it, Sr Isaac replied immediately that it would be an Ellipsis…”[1] The description of Newton given by Cosmos introducing this fateful meeting also owes more to fantasy than reality. We get told that Newton went to pieces over his dispute with Hooke concerning his theory of light, that he had become a recluse and that he was in hiding in Cambridge. Although Newton declined to have anything more to do with the Royal Society following the numerous disputes, not just with Hooke, following the publication of his theory of light in 1672 he certainly did not go to pieces, giving as good as he got and he was not hiding in Cambridge but working there as Lucasian Professor of Mathematics. Also far from being a recluse he was corresponding with a wide range of other scholars, including Hooke with whom he had sealed an uneasy truce. Blatant misrepresentations might be all right in a historical novel but not in a supposedly serious television documentary claiming to present history of science.

We now move on to the writings that Newton’s meeting with Halley provoked. First we get shown Du motu corporum in gyrum (On the Motion of Bodies in Orbit) a nine page pamphlet demonstrating the truth of Newton’s statement and quite a lot more, although Tyson doesn’t think it necessary to give us either the title or a description of the contents calling it instead, “the opening pages of modern science”, a truly crap statement. If De motu represents the opening pages of modern science what was all the stuff that Kepler, Stevin, Galileo, Pascal, Descartes, Mersenne, Huygens et al. did? Most of it before Newton was even born! There is worse to come.  In the Cosmos version of the story Halley now urges Newton to turn De motu into a book, in reality Halley wanted to enter De motu officially in the Royal Society’s register “to secure his [Newton’s] invention to himself” and it was Newton who insisted on rewriting it. It was this rewritten version that became Principia Mathematica. When almost complete the council of the Royal Society agreed that it should be published by the Society. At this point the proverbial shit hit the fan. As related in Cosmos, Hooke raised a claim to the theory of gravity and demanded that Newton give him credit for it in his book. Newton’s prickly response was to threaten to withhold volume three of the Principia, which is actually the part in which he applies his theories of motion and the law of gravity to the celestial motions i.e. the heart of the whole thing. Tyson now said, “The scientific revolution hung in the balance”! I said worse was to come.

According to convention wisdom the scientific revolution began in 1543 with the publication of Copernicus’ De revolutionibus. I’m a gradualist who doesn’t accept the term scientific revolution and for me the evolution of modern science begins around fourteen hundred although it builds on earlier medieval science. For most historians Newton’s Principia is the culmination not the beginning of the scientific revolution. It was even fashionable for a time to play down Newton’s achievement claiming that he only synthesised the result won by his predecessors. However it is now acknowledged that that synthesis was pretty awesome. However let us play a little bit of what if. If Newton had only published the first two volumes of Principia I doubt that it would have been very long before somebody applied the abstract results derived in volume one to the solar system and completed what Newton had begun. Put another way nothing hung in the balance.

In fact Halley was able to mollify Newton and the letters that the two of them exchanged at this time are the main historical source for the whole story. Cosmos paints Hooke as an unmitigated villain at this point in the story, which is again a distortion of the true facts. Hooke had indeed suggested, in print, a universal theory of gravity based on the inverse squared law and the letters he exchanged with Newton, during the uneasy truce mention above, had played a significant role in pushing Newton towards his own theories of motion and gravity. Hooke’s claim was not totally unfounded. It is true, however, that his claim was exaggerated because he did not possess the mathematical skills to turn those hypotheses into the formal mathematical structure that is the glory that is Newton’s Principia. There was blame on both sides and not just on Hooke’s. Cosmos now introduces a strange scene in which Wren and Halley meet up with Hooke and confront him on the gravity priority issues, Halley even telling Hooke to “put up or shut up”! Numerous people on Twitter commented on this sound bite, most of them betting that Halley never said it. Not only did Halley never say it, the whole scene is a product of the scriptwriter’s fantasy; in reality it never took place. Remember this is supposed to be history of science and not historical fiction.

With then get treated to the infamous History of Fish episode. In 1685 the Society had published Francis Willughby’s De historia piscium, which had been finished and edited posthumously by John Ray. The book having many lavish illustrations was costly and sold badly putting a serious strain on the Society’s, in the seventeenth-century always dodgy, finances leaving no money to fulfil the commitment to publish Newton’s Principia. This is a well-known and oft repeated story and mostly told at the cost of Willughby and his book. Cosmos did not deviate from this unfortunate pattern telling the story in a heavy handed mocking style. For the record Willughby’s book is an important publication in the history of natural history and deserves better than the treatment it got here.

Before we leave Newton and his masterwork we get presented with yet another historical clangour of mindboggling dimensions. Tyson informs us in his authoritative manner that Principia also contains Newton’s invention of the calculus. Given the amount of printer’s ink that had been used up in the academic discussion as to why Newton wrote the Principia in Euclidian geometry and not calculus this is an unforgivable gaff. I repeat for those who have not been paying attention there is no calculus in Newton’s Principia.

We now leave Newton and turn our attention to his sidekick Edmond Halley. We get a brief presentation of some of the non-astronomical aspects of the good Edmond’s life, which also contain several minor historical errors that I can’t be bothered to deal with here, before turning to the central theme of the programme, comets. There is however one major astronomical subject that I cannot ignore, the Transit of Venus. It was not, as claimed, Halley who first proposed using the Transit of Venus to determine the astronomical unit, the distance of the sun from the earth, but James Gregory in his Optica Promota published in 1663. We then get presented with the rather strange spectacle of James Cook sailing off to Tahiti in 1769 to observe the Transit. This is strange not because it’s wrong, it isn’t, Cook did indeed observe the Transit on Tahiti in 1769 but because the programme created the impression that he was the first and only person to do so. In reality Cook’s expedition was only one of many international expeditions that took place in 1769 for this purpose also there had been almost as many expeditions that had set out for the same purpose in 1761. We do not owe our knowledge of the size of the astronomical unit to some sort of solo heroic efforts of Cook in 1769 as implied by Cosmos.

The opening section of the episode was actually very well scripted with a sympathetic and understanding explanation as to how humanity came to view comets as harbingers of doom. Unfortunately this good beginning was ruined by the claim that was repeated several times throughout the script that it was Newton and Halley who were the first to view comets as astronomical objects and thus free humanity from its superstitious fear. This is just plain wrong.

In the Early Modern Period Paolo dal Pozzo Toscannelli was the first to make astronomical observations, as opposed to superstitious wonderings, of two comets in 1433 and 1456. He did not publish those observations but he did befriend Georg Peuerbach on his study journey through Renaissance Italy. Peuerbach and his pupil Regiomontanus made similar observations in Vienna in the middle of the fifteenth-century and Regiomontanus wrote an important text on the mathematical problem of measuring the parallax of a moving comet, which wasn’t published in his own lifetime.

In the 1530s several European astronomers carried out astronomical observations of a series of spectacular comets. This period led to Johannes Schöner publishing Regiomontanus’ comet text. Peter Apian published a pamphlet on his observations describing, what is incorrectly known as Apian’s Law because it was already long known to the Chinese, that the comet’s tail always points away from the sun. This series of comets and the observations of them led to an intense scientific discussion amongst European astronomers as to the physical nature of comets and their position in the heavens, above or below the moon, sub- or supra-lunar? Fracastoro, Frisius, Cardano, Jean Pena and Copernicus took part in this discussion.

In 1577 astronomers throughout Europe again observed a spectacular comet to test the theories proposed by those who had taken part in the 1530s discussions. Famously Tycho Brahe and Michael Maestlin, amongst others, determined that this comet was definitely supra-lunar. In the same period Brahe and John Dee corresponded on the subject of Regiomontanus’ comet text, the determination of cometary parallax.

Cometary observation again hit a high point in astronomical circles in 1618. The comets of this year famously led to the dispute between Galileo and the Jesuit astronomer Orazio Grassi that culminated in Galileo’s Il Saggiatore, one of the most often quoted scientific publications of all times. They also saw the publication of a much more low-key text, Kepler’s book on comets published in 1619. Kepler summarised in his work all of the astronomical knowledge on comets that had been gained in the Early Modern Period, concluding himself that comets are supralunar and travel in straight lines. Ironical someone else had suggested that comets follow Keplerian elliptical orbits eight years earlier. Thomas Harriot and his pupil William Lower had observed the comet of 1607, Halley’s comet, and were amongst the first to read Kepler’s Astronomia nova when it appeared in 1609 and to become convinced Keplerians. In a letter to Harriot, Lower suggested that comets, like the planets, have elliptical orbits. Lower’s suggestion did not become generally known until the nineteenth century but it shows that the discussion on the flight path of comets was already in full swing at the beginning of the seventeenth-century.

With the comets of the 1660’s the debate on the nature of comets and their flight paths again broke out amongst the astronomers of Europe with Kepler’s comet book at the centre of the debate, so when Newton and Halley entered the fray in the 1680s they were not initiating anything, as claimed by Cosmos, but joining a discussion that had been going on for more than two hundred years. A final omission in the Cosmos account concerns another man with whom both Halley and Newton would become embroiled in bitter disputes, the Astronomer Royal John Flamsteed. The early 1680s saw a series of spectacular comets that Flamsteed observed from Greenwich and Halley from Paris.  Flamsteed concluded that two of these were in fact one and the same comet first observed on its way to the sun and then again on its way away from the sun having passed behind it. He reported this theory to Newton who at first rejected it but then on further consideration accepted and adopted it, making comets a central theme for his research for the Principia, utilising Halley as his assistant for this work. That comets follow flight paths described by the various conic sections depending on their velocities, some of them elliptical, under the influence of the law of gravity is a central element of volume three of Principia and not something first determined by Halley in his 1705 paper as claimed by Cosmos. Halley undertook his research into the historical records of comets to see if he could find a reoccurring comet to confirm the theory already presented in Principia, as everybody knows he was spectacularly successful.

Having completely messed up the history of astronomical cometary observation Cosmos closed by returning to the Newton Hooke dogfight. We get told Hooke died in 1703 as a result of his unhealthy habits of doctoring himself with all sorts of substances. Given that Hooke lived to the age of 67, not at all bad for the seventeenth-century I found this to be an unnecessary slander on the poor man. Tyson then went on to say that Newton replaced him as President of the Royal Society. Robert Hooke was an employee of the Royal Society and never its President. Newton in fact followed Lord Somers in this august position. Although hedged with maybes, we then got the old myth of Newton burning Hooke’s portrait dished up once again. On this hoary old myth I recommend this post by good friend Felicity Henderson (@felicityhen) on her Hooke’s London Blog (always well worth reading). Given the vast amount of real history of science that they could have brought I don’t understand why Cosmos insists on repeating myths that were discredited long ago.

The history of science presented in this episode of Cosmos was shoddy, sloppy, badly researched, factually inaccurate and generally of a disgustingly low level. On Twitter the history of science hashtag is #histsci, historian of biology Adam Shapiro (@TryingBiology) suggested that the hashtag for Cosmos history of science should be #HistSigh, I concur.

 

[1] Richard S. Westfall, Never at Rest: A Biography of Isaac Newton, Cambridge Paperback Library, Cambridge University Press, 1983, p. 403. Quoting Abraham DeMoirve’ s account of the meeting as related to him by Newton.

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Filed under Early Scientific Publishing, History of Astronomy, History of science, Myths of Science, Renaissance Science

SHOCK! HORROR! OUTRAGE! RELIGION HINDERS PROGRESS OF SCIENCE!

The title is supposed to make you think of a typical article in the Daily Fail, Britain’s most obnoxious representative of the gutter press. It represents one of the dominant reactions by members of the Gnu Model ArmyTM to the Cosmos Bruno AffairTM. According to people such as Jason Rosenhouse and P Z Myer the persecution of such notable scientists as Giordano Bruno and Galileo Galilei by the Catholic Church has definitely hindered the progress of science and for good measure they or their supporters quote the words of wisdom of Über-Guru Neil deGasse Tyson that without religion science would be a thousand years more advanced. What an outrage, truly horrific the Church it seems has a lot to answer for, although I find it rather strange that they can’t dish up more examples than poor old Giordano and that universal symbol of Church oppression Galileo. I’m sure if they re-read their Draper-White they could manage to find some new names to beat the ignorant historians around the head with. I say ignorant historians because it was the historians complaining about the Bruno cartoon on the first episode of Cosmos that has brought out this charge by these stalwart defenders of scientific integrity.

Let us assume for a moment that Rosenhouse-Myer are correct and that the Catholic Church did in fact persecute Bruno and Galileo to block scientific progress does this necessarily mean that they were successful in their dastardly deeds? Did they truly manage to interrupt, slow down, or hinder the adoption, acceptance or acknowledgement of the heliocentric hypothesis or the belief in an infinite universe or the perception that the sun is a star or vice versa? No doubt about it, this is a serious charge and one that should definitely be explicated.

Now Myer and Tyson are both practicing scientists whilst Rosenhouse is a mathematician, all of them work in disciplines that require one, if one makes a substantial claim, to provide the appropriate evidence or proof to support that claim. What is with their claim that religion has blocked the advance of science in general or in the case of Bruno and Galileo the acceptance of modern astronomy and cosmology in particular? Have our scientific practitioners provided the necessary evidence to back up their claims? Do they provide a tightly argued historical thesis based on solid documentary evidence to prove their assertions? Can they demonstrate that if the Church had not intervened modern astronomy would have become accepted much earlier than it was? Given their outspoken support of the ‘scientific method’, whatever that might be, you would expect them to do so, wouldn’t you? Do they hell! They don’t waste one single word on the topic. No evidence, no proofs, no academic arguments just plain straightforward unsubstantiated claims in the style of the gutter press. A pretty poor showing for the defenders of scientific faith.

But could they still be right? Even if they don’t take the trouble to provide the historical discourse necessary to substantiate their claims, could it be true that the Church’s actions against Bruno and Galileo did in fact have a negative influence on the acceptance of heliocentricity and other aspects of modern astronomy and cosmology? Let us examine the historical facts and answer the questions that Rosenhouse-Myer and Tyson are apparently above answering, the truth being apparently so obviously clear that they don’t require answering.

To start with the poor Giordano, Bruno was one of those who advocated Copernicus’ heliocentric astronomy already in the sixteenth-century. He however went beyond Copernicus in a series of cosmological speculations and it is these that Cosmos thought to be so important that they devoted eleven minutes of a forty-five minute broadcast to them. I shall deal with the acceptance of heliocentricity separately later and only address Bruno’s cosmology now. Copernicus himself expressly left the question as to whether the cosmos is finite or infinite, as he said, to the philosophers, with good reason. This question was purely speculative and could not, with the evidence and possibilities available to the Renaissance astronomer, be addressed in anything approaching a scientific manner. To all intents and purposes the cosmos appeared finite and Renaissance scholars had no means available to prove otherwise. Bruno’s speculation was of course not new.

In his own times Nicolas Cusanus had already considered the question and earlier, in the first-century BCE, the Epicurean philosopher poet Lucretius, Bruno’s inspiration, had included it in his scientific poem De rerum natura. Lucretius of course did not invent the concept but was merely repeating the beliefs of the fifth-century BCE Greek atomists. All of this demonstrates that the idea of an infinite cosmos was fairly common at the beginning of the seventeenth century and nothing the Church said or did was likely to stop anybody speculating about it. The thing that prevented anybody from going further than speculation was the lack of the necessary scientific apparatus to investigate the question, a similar situation to that of the string-theorists and multiverse advocates of today.

This does not mean that astronomers did not address the problem of the size of the cosmos and the distance to the stars. Amongst others Galileo, Jeremiah Horrocks, Christiaan Huygens and Isaac Newton all tried to estimate/calculate the distances within the solar system and outward towards the stars. First in the middle of the eighteenth century with the transit of Venus measurements were these efforts rewarded with a minimum of success. It wasn’t until the early nineteenth century that the first stellar distance measurements, through stellar parallax, were achieved. All of these delays were not caused by anything the Church had done but by the necessity of first developing the required scientific theories and apparatus.

Bruno’s next cosmological speculation was that the sun and the stars were one and the same. Once again there was nothing new in this. Anaxagoras had already had the same idea in the fifth-century BCE and John Philoponus in the fifth-century CE. Once again the problem with this speculation was not any form of religious objection but a lack of scientific theory and expertise to test it. This first became available in the nineteenth century with development of spectroscopy. This of course first required the development of the new matter theory throughout the seventeenth and eighteenth centuries, a process that involved an awful lot of science.

Bruno’s last speculation and the one that bothered the Church was the existence of inhabited planets other than the Earth. Again this was nothing new and whatever the Church might have thought about it that speculation generated a lively debate in the seventeenth century that is still going on. We still don’t actually know whether we are alone or not.

Given my knowledge of the history of science I can’t see anywhere, where the Church hindered or even slowed down scientific progress on those things that Bruno speculated about in his cosmological fantasy. But what about heliocentricity, here surely the Church’s persecution of both Bruno and Galileo hindered science bay the hounds of anti-religious rationalism.

What follows is a brief sketch of the acceptance of the heliocentric astronomy hypothesis in the sixteenth and seventeenth centuries. This is a subject I’ve dealt with before in various posts but it doesn’t hurt to repeat the process as there are several important lessons to be learnt here. To begin with there is a common myth that acceptance of ‘correct’ new scientific theories is almost instantaneous. To exaggerate slightly, Einstein published his General Theory of Relativity in 1915 and the world changed overnight or at the latest when Eddington confirmed the bending of light rays conform with general relativity in 1919. In reality the acceptance of the general theory of relativity was still a topic of discussion when I was being educated fifty years later and that despite numerous confirmatory tests. Before it is accepted a major new scientific theory must be examined, questioned, tested, reformed, modified and shown to be superior to all serious alternatives. In the Early Modern Period with communication considerably slower this process was even slower.

Copernicus published his De revolutionibus in 1543 and there were only ten people in the entire world, including Bruno but much more importantly both Kepler and Galileo, who accepted it lock, stock and barrel by 1600. This system had only one real scientific advantage over the geocentric one; it could explain the retrograde movement of the planets. However this was not considered to be very important at the time. There were some relatively low-key religious objection but these did not play any significant role in the very slow initial acceptance of the theory. The problematic objections were observationally empirical and had already been discussed by Ptolemaeus in his Syntaxis Mathematiké in the second-century CE. Put very simple if the world is spinning very fast and hurtling through space at an alarming speed why don’t we get blown away? Copernicus had the correct answer to this problem when he suggested that the atmosphere was carried round with the earth in the form of a bubble so to speak. Unfortunately he lacked the physics to explain and justify such a claim. It would take most of the seventeenth century and the combined scientific efforts of Kepler, Galileo, Stevin, Borelli, Descartes, Pascal, Huygens, Newton and a whole boatload of lesser lights to create the necessary physics to explain how gravity holds the atmosphere in place whilst the earth is moving.  This process was not hindered by the Church in anyway whatsoever.

There was a second level of acceptance of Copernicus theory, an instrumental one, as a mathematical model to deliver astronomical data for various applications, astrology, cartography, navigations etc. Here the system based on the same inaccurate data as the Ptolemaic one did not fair particularly well. Disgusted by the inaccuracy of both systems Tycho Brahe started a new long-term observational programme to obtain new accurate data. Whilst doing so he developed a third model, the so-called geo-heliocentric model, in which the planets orbited the sun, which in turn orbited the stationary earth. This model had the advantage of explaining retrograde motion without setting the earth in motions, a win-win situation.

The first major development came with the invention of the telescope in 1608 and its application to astronomical observation from 1609 onwards. The first telescopic discoveries did not provide any proofs for either the Copernican or the Tychonic models but did refute both the Aristotelian homocentric model and the Ptolemaic model. Around the same time a new candidate, the Keplerian elliptical astronomy, entered the ring with the publications of Kepler’s Astronomia nova in 1609. For a full list of the plethora of possible astronomical models at the beginning of the seventeenth century see this earlier post.

By 1620 the leading candidate was a Tychonic model with diurnal rotation. It should be pointed out that due to the attempts of Galileo and Foscarini to reinterpret Holy Scripture in favour of heliocentricity the Catholic Church had entered the action in 1615 and forbidden the heliocentric theory but not the heliocentric hypothesis. The distinction is important. The theory says heliocentricity is a scientific fact the hypothesis says it’s a possibility. At this time heliocentricity was in fact an unproved hypothesis and not a theory. This is the point where Rosenhouse-Myers step in and claim that the Church hindered scientific progress but did they. The straightforward answer is no. The astronomers and physicist carried on looking for answers to the open questions and solutions to the existing problems. There is no evidence whatsoever of a slowing down or interruption in their research efforts.

Between 1618 and 1621 Kepler published his Epitome astronomiae Copernicanae explaining his elliptical astronomy and his three laws of planetary motion in simple terms and in 1627 the Tabulae Rudolphinae the astronomical tables based on his system and Tycho’s new accurate data. It was these two publications that would lead to the general acceptance of heliocentricity by those able to judge by around 1660. Kepler’s publications delivered the desired accurate prognoses of planetary positions, eclipses etc. required by astrologers, cartographers, navigators etc.

At no point in the 120 years between the initial publication of Copernicus’ De revolutionibus and the general acceptance of heliocentricity in the form of Kepler’s elliptical astronomy is there any evidence of the Church having slowed or hindered progress in this historical process. To close it should be pointed out that it would be another seventy years before any solid scientific evidence for the heliocentric hypothesis was found by Bradley, in the form of stellar aberration.

 

 

 

 

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Filed under History of Astronomy, History of science, Myths of Science, Uncategorized

A strange defence

This week saw the broadcast of the first episode of the remake of the legendary television series COSMOS, originally hosted by Carl Sagan and now being presented by Neil deGasse Tyson. Although I have now had the chance to view it thanks to the good offices of the man for all things Darwinian, Michael Barton (@darwinsbulldog), I’m not going to blog about it as Tim O’Neill, Renaissance Mathematicus reader and commentator, and fellow invincible warrior in the struggle against bad history of science,  is writing a guest post on the subject, which if all goes well will appear here on next Monday. However this post is directly concerned with one part of the show.

The centrepiece of the episode was an anime style carton on the life and thoughts of infamous Renaissance heretic Giordano Bruno. This immediately led to a raising chorus of voices on Twitter wondering what my views on this would be. Having in the mean time seen it I labelled it on Twitter an “Anime Draper-White for the Twenty-First Century”. For anybody who doesn’t know John William Draper (1811 – 1882) and Andrew Dickson White (1832 – 1918) are the two nineteenth century American academics who created the myth of a war (their term) between science and religion. A myth still unfortunately believed in by many a gnu atheist.  I’m not going to say anything more about this unfortunate piece of animated bollocks, as I’m sure that Tim will comment extensively in his guest post.

However the rest of the Intertubes has not remained silent on the issue and I can recommend the eminently sensible post on the subject by Meg Rosenburg (@trueanomalies) and the wonderfully provocative post by Becky Ferreira (@beckyferreira) “What ‘cosmos’ got wrong about Giordano Bruno, the heretic scientist, which contains the absolutely brilliant description of Bruno: “Bruno was a walking, talking shit storm, with a black belt in burning bridges”.  How I wish that I had coined that sentence!

The debate continued at Discovery Magazine with a blog post by Cory S. Powell, “Did “Cosmos” pick the wrong hero?”, in which Powell suggests that Thomas Digges would have made a better subject for the cartoon than Bruno. Personally I side with Meg Rosenburg who asks whether we need any heroes at all when discussing the history of science; a rhetorical question to which the answer is no.

Powell’s post finally provoked a response from the makers of “Cosmos” in the form of a post by Steven Soter, astrophysicist and co-writer of “Cosmos”, titled The Cosmos of Giordano Bruno (now with added response from Powell) and it is to this post that I now wish to reply, as it contains a number of very questionable statements.

In his second paragraph Soter writes the following:

Powell’s critique dwells on the well-known facts that Bruno was a mystic and an extremely difficult person. Well, so was Isaac Newton, who devoted as much time to alchemy and biblical numerology as to physics. But that has no bearing whatever on his good ideas.

I could write a whole post just about this one paragraph. First off Soter is putting Bruno a man who had one half correct cosmological idea during an intoxicating religious fantasy, that makes you wonder if he’d been hitting the magic mushrooms, with Isaac Newton who produced some of the most important new mathematics, astronomy, and mathematical physics in the history of mankind. That’s one hell of a lopsided analogy Mr Soter! Secondly as anybody knows, who is up to date on his Newton research, or who has simply read some of my blog posts on the man, Newton’s theology and his alchemy did have a massive bearing on his ‘good ideas’.

Soter then corrects Powell as to who first claimed that the universe was infinite, which to be fair Powell got wrong, although neither of them remarks that Lucretius, Bruno’s source, didn’t think of this himself but actually got the idea from the Greek atomists.

We now come to the core of the matter and the reason why Soter et al claim to have included the Bruno cartoon in their show:

Bruno’s originality lies elsewhere. He was indisputably the first person to grasp that the Sun is a star and the stars are other suns with their own planets. That is arguably the greatest idea in the history of astronomy. Before Bruno, none of the other Copernicans ever imagined it.

Leaving aside the hyperbole about ‘the greatest idea in the history of astronomy’, as he says the question is highly debateable, this paragraph still has several issues. Firstly the Greek philosopher Anaxagoras had already suggested that the sun and the stars were one and the same in the fifth century BCE, although he didn’t hypothesise the presence of other planets. Secondly if this was the real reason for including the Bruno cartoon in this episode, why was the main emphasis of the cartoon placed on the Church’s treatment of Bruno as a heretic even to the extent of presenting the Church officials as demons with red glowing eyes, I smell a rat.

If you think I’m misinterpreting the message of the cartoon I offer this comment from Meg Roserburg’s post, Albeit says:

No offense, but I think you’re missing the point here. The moral of the story, as stated in Cosmos, is: don’t let your beliefs stand in the path of reality. Bruno’s necessarily oversimplified story is just a warning about anti-science and dogmatic thinking.

Throughout the Internet you can find similar interpretations, so either the message of the cartoon was other than claimed by Soter or they really made a balls up of scripting it.

Soter than attacks Powell’s suggestion that Thomas Digges should have been featured rather than Bruno, after all he did suggest that the universe is infinite before Bruno. Soter’s argument is a little strange he writes:

But Digges regarded the stars as “the court of the celestial angels” not as the suns of other material earths. And that was a big step backwards. In contrast, Bruno wrote, “the composition of our own stars and world is the same as that as many other stars and worlds as we can see.” His profound intuition had to wait three centuries to be verified by the spectroscope.

First off Digges’ claim that the stars were the court of the celestial angels is just bog standard medieval cosmology, so in that sense is not a step backwards. Secondly Digges wrote and published earlier than Bruno, so in that sense it is also not a step backwards.

That the composition of everything in the cosmos was the same is neither new nor original to Bruno. The Stoics had believed this in antiquity and there had been a major revival in Stoic scientific philosophy in the sixteenth century making Bruno considerably less original on this count than Soter would like to see him.

Soter is also guilty here of quote mining, selecting those parts of Bruno’s fantasy that fit with our modern concepts and quietly ignoring those that don’t. This is a form of presentism known as searching for predecessors. One takes an accepted scientific idea and filters through history to see if somebody had the same idea earlier, then crying eureka and declaring the discovered thinker to be a genius ahead of his or her times. This activity can best be observed in popular histories of atomism where everybody who ever believed that matter consists of some sort of particles are all swept up into one glorious heap and declared to be predecessors of John Dalton. In Bruno’s case one has to ignore the rather inconvenient fact that he thought that the whole of space was filled with identical solar systems placed throughout space at equal intervals, a conception that doesn’t quite fit with our actually understanding of the universe.

Soter now attacks Powell for saying that neither Kepler nor Galileo thought much of Bruno. Soter mocks and ridicules Kepler for believing in a finite universe.  This is ironic given that Soter thinks it is irrelevant that Bruno produced fifty tons of shit including rejecting the use of mathematics in science because he produced one tiny little diamond of thought.

Soter then quote mines again making Kepler to a supporter of Bruno. He correctly quotes a passage from Kepler’s Dissertatio cum Nuncio Sidereo (1610) his response to Galileo’s telescopic discoveries.

What other conclusion shall we draw from this difference, Galileo, than that the fixed stars generate their lights from within, whereas the planets, being opaque, are illuminated from without; that is, to use Bruno’s terms, the former are suns, the latter, moons or planets?

Here Kepler is referring to the difference in the images of planets and stars when viewed through the new invention the telescope. Kepler would here be appearing to support Bruno’s theory and that is the impression that Soter wisher the reader to have but this is actually an illusion. Kepler says let us use Bruno’s term, he doesn’t say let us adopt Bruno’s theory. You might think I’m splitting hairs and that by adopting Bruno’s term Kepler is of course adopting Bruno’s theory but this is very definitely not the case. How can I be so sure? Because Kepler himself tells us so, he does so by evoking what is now known as Olbers’ paradox.  Kepler argues, as did Heinrich Olbers, a German astronomer, in the nineteenth century, that if the heavens were filled with an infinity of suns equally distributed in all direction, as Bruno claimed, then there would never be a night, these suns lighting up the skies twenty-four hours a day. His, incorrect but rational solution, to the paradox was that the Sun and the stars are fundamentally different and thus Bruno was wrong. Far from being a tacit supporter of Bruno’s hypothesis, as Soter would have us believe, Kepler actually refuted it with a good solid, if incorrect, scientific argument. A further irony in this situation is that Kepler was not the first to realise that an infinity of suns would lead to Olbers’ paradox, thus seeming to invalidate Bruno’s hypothesis, Thomas Digges, who hypothesised an infinity of stars before Bruno, also explicitly recognised the problem.

Having abused Kepler Soter now moves on to Galileo accusing him of plagiarism and cowardice, in the process again making a false claim:

Galileo never once mentioned Bruno’s name. Of course in the land of the Inquisition he had good reasons. But in his “Dialogue on the Two Chief World Systems” (the book that got him into deep trouble), he discretely accepted Bruno’s greatest idea, writing that the fixed stars are other suns.

Don’t let anybody tell you that being a pedantic history of science blogger is an easy life. Although I possess two different translations of Galileo’s magnum opus I don’t know it off by heart and was not aware of Galileo “discretely accepting Bruno’s greatest idea”, so I spent about four hours yesterday evening going through every single reference to star, stars or sun listed in the index to the Drake translation comparing with the Finocchiaro translation and searching for further information in five volumes of secondary literature. The only consolation for all of this effort was that I found the passage to which Soter is probably referring. On The Second Day in a discussion on the movement of the heavenly bodies Salviati makes the following observation:

Now behold how nature, favoring our needs and wishes, presents us with two striking conditions no less different than motion and rest; they are lightness and darkness – that is, being brilliant by nature or being obscure and totally lacking in light. Therefore bodies shining with internal and external splendour are very different in nature from bodies deprived of all light. Now the earth is deprived of light; more splendid in itself is the sun, and the fixed stars are no less so. The six moving planets entirely lack light, like the earth; therefore their essence resembles the earth and differs from the sun and the fixed stars: Hence the earth moves and the sun and the stellar sphere are motionless.

This passage is, like the Kepler quote above, very clearly based on Galileo’s telescopic observations of the stars and planet and their respective telescopic images and is not borrowed from Bruno. It is also clear that here Galileo is only referring to the stars and the sun both being self-illuminating, his discussion only treats of one attribute, lightness or darkness, but he doesn’t take the next step of saying that therefore they are the same. He might possibly have thought so but then again he might not. It is also clear here that with his reference to the stellar sphere Galileo s still accepting a traditional bounded finite cosmos.

I now turn to the implicit argument that Galileo didn’t reference Bruno because of the Inquisition, either through caution or, as I provocatively said above, through cowardice. This argument is not unique to Soter but has been used by numerous commentators in the Internet in the last few days. In the Roman Inquisition had, like the FBI, had a Most Wanted list, then during the first part of Galileo’s life Numero Uno on that list would have, without any doubt, been the Servite monk Paolo Sarpi (1552 – 1623).  To quote John Heilbron’s Galileo biography, “…the Servite Sarpi, would present the Vatican with a graver threat than Bruno”. During his years in the Republic of Venice, as professor of mathematics at the University of Padua, Galileo’s best mate and intellectual sparing partner was Sarpi, a fact that was publically well known. Unlike Bruno, who they regarded as a nuisance, the Venetian authorities, who were very proud of their intellectual rebel, Sarpi, who was Venetian born and bred, refused to deliver him to the Roman Inquisitions. Making him even more of a thorn in the side of the Church. Galileo’s close friendship to Sarpi was far more dangerous to his relations with the Church than any casual scientific reference to Bruno would have been. Galileo did not quote Bruno because he didn’t want to, not because he was scared of the Inquisition.

It is worth noting in this context that when Galileo applied for and was granted the position of court philosophicus and mathematicus to the Medici in Florence his Sarpian friends in Venice warned him against leaving the comparatively safe haven of thr Republic, where he was free to think and say almost anything he liked, for the shark infested waters of court intrigue and religious orthodoxy of Florence and Rome. However fame, fortune and social status were more important to Galileo than freedom of thought and speech so he ignored his friends’ warnings with the well known historical consequences.

To close this already over long post I would like to address a historiographical point related to Soter’s deification of Bruno in the history of science. Wirkungsgeschichte is a German term that refers to the historical impact of a scientific theory, invention, or discovery. Some ideas make little or no impact and disappear from the historical stage requiring them to be rediscovered at a later date. A classic example of this is the correct explanation of the cause of the rainbow. Theodoric of Freiberg discovered the correct explanation through empirical experiments in the thirteenth century. However his discovery had almost no impact and got lost, meaning that it wasn’t until the seventeenth century, when Descartes rediscovered it, that the correct explanation of the rainbow became generally known. Bruno’s lucky guess that the stars are suns or that the sun is a star had almost no impact and was largely ignored and forgotten. This makes him in a historical sense a dubious figure to elevate to the status of a scientific hero, as Soter apparently wished to do with his very strange animation in the COSMOS broadcast.

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Filed under History of Astronomy, History of science, Myths of Science, Renaissance Science

Why Newton’s Apple is not a good story.

Over on the Scientific American Guest Blog we have another non-historian trying his hand at the history of science under the title Newton’s Apple: Science and the Value of a Good Story. Our author, Ned Potter a Senior Vice President of an international communications firm and former science correspondent, tells us that Isaac Newton almost invariably tops any list of history’s greatest scientists and then poses the question, why? His answer is that Newton had a great story to tell:

It’s the one about the apple. You remember it – how the young Newton, sent home from school at Cambridge to avoid the plague of 1665, was sitting under a tree one day, saw an apple fall to the ground, and, in a flash of insight, came to understand the workings of gravity.

Right there in his retelling, Potter, reveals why Newton’s Apple is anything but a great story but before I explain why, I have other fish to fry. In a lackadaisical paragraph our intrepid author summarises Newton’s scientific career:

He published his Principia Mathematica in 1687. In his spare time he designed the first reflecting telescope, laid the foundations for calculus, brought us the understanding of light and color, and in his later years – it would be disingenuous to leave this out – tried his hand at alchemy and assigning dates to events in the Bible.

He did not design the first reflecting telescope in his spare time. Investigating the nature of light and colour was at the centre of his scientific endeavours twenty years before he composed the Principia Mathematicae and his design of the reflecting telescope was his answer to the problem of chromatic aberration in lenses that his new theories on colour had discovered and explained. It also wasn’t the first reflecting telescope but the first functioning one, as I’ve already explained elsewhere. Laying the foundations of calculus was also not a spare time activity. We now turn to something that I’m slowly getting tired of correcting. Newton did not try his hand at alchemy and assigning dates to events in the Bible in his later years but started both activities in his youth continuing them for many years. They also played a very central role in the heuristics of his scientific research, as I’ve said on more than one occasion.

My readers may ask themselves why the dating of Newton’s, by modern standards, non-scientific activities is such an important subject for me. It’s rather the other way around. By pretending that Newton only did these things in his dotage people like Potter came claim that Newton was a rational modern scientist in his youth who went off the rail in his old age, poor man. This is the creation of a myth in the history of science. Newton’s alchemy, theology and chronology are a central part of what made him the scientist that he was, to deny this is to deny the man himself and to put a mythological figure, who never existed, in his place. That is not doing history of science and should also have no place in the popular presentation of science.  But back to Newton’s Apple!

The offending phrase is of course saw an apple fall to the ground, and, in a flash of insight, came to understand the workings of gravity. This is not what happened and it also creates a completely false impression of the scientific process of discovery.  Nobody, not even Newton, understands a complex scientific theory such as the theory of universal gravity in a flash of inspiration and claims that they do misinform non-scientists about how science works.

Assuming the apple story to be basically true, and there are many historian of science who think that it is a myth, what Newton thought is very different to coming to understand the workings of gravity in a flash of insight. The sight of the falling apple led him to pose a question to himself, something along the lines of, ”what causes the apple to fall to the ground?” This led to another question, and herein lies Newton’s brilliance, is that which causes the apple to fall downwards the same as that, which prevents the moon from shooting off in a tangent to its orbit as the law of inertia say it should? Here we have the beginning of an idea that can only have taken place in a mind prepared by the requisite study to be able to form this particular idea. The idea alone is in itself useless unless one possesses the necessary knowledge to test it. Newton did possess this knowledge of dynamics, astronomy and mathematics, which he had acquired through intensive personal study over the previous years rather than from his university lecturers. He then applied this knowledge to testing his newly won hypothesis, a fairly complex and demanding mathematical calculation that required both time and effort. And see here the result!  The two aren’t the same! Newton’s initial attack on the problem failed because of inadequate data. He put the problem aside and devoted himself instead to the study of optics (see above). However he did not forget that insight and many years later he returned to the problem with fresh data and showed that his initial insight had in fact been correct. The way was now open to the development of the universal theory of gravity. Note after all of the steps that we have already gone through we have not arrived at the workings of the theory of gravity, we have merely started down the road towards it. In fact Newton would have to invest two years of very intense work, to the exclusion of everything else in his life, between 1684 and 1687 in order to finally develop the theory in all of its glory, as published in his Principia. The process can hardly be described as “a flash of insight”.

I hope that I have made clear that, in the sense of Ned Potter, Newton’s Apple is anything but a good story, as it creates a complete misconception of the scientific process, a process that even in the case of a monster intellect such as Newton’s involves an incredible amount of study and sheer hard work.

The story as presented by Potter could however have its uses in teaching an introductory course in the history of science and in illustrating the scientific process. One presents the students with the myth of Newton’s Apple à la Potter and then have them research the real historical situation. To look for, read and analyse the original sources of the apple story, William Stukeley, as well as John Conduit and Voltaire, who both had the story from Catherine Barton, Newton’s niece and housekeeper as well as Conduit’s wife. Then have them study the real process by which Newton developed his theory of universal gravity, as I have sketched it, demonstrating how misleading such tales can be. As such I think that the Newton’s Apple story can be put to good pedagogical use, however as Potter wishes it to be considered:

Over the years, inevitably, the details have been embellished. Ask around today, and people may tell you that the apple bonked Newton on the head. But the point remains: if you have an important point to make, especially in science but also in other fields, there’s nothing like a good story to make it memorable.

I think it’s anything but a good story particularly if the important point being made is completely false.

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Filed under History of science, Myths of Science, Newton

OPUS 500: A retrospective

This is, and I don’t really believe it myself, the five hundredth post here at the Renaissance Mathematicus. This is generally regarded as an important milestone, half way to the thousand, a five followed by not one but two zeros. Actually it’s is just a number like any other number and the significance that we attribute to it is purely the result of the fact that we have ten digits and therefore have developed and adopted a decimal place value number system. If we had been born with twelve fingers instead of ten then this would only be the 358th post and we would have nothing to celebrate. Somewhere within its twisted circuits, my computer has this registered as the 111110100th post.

On the other side although this is the five hundredth post, not all of those five hundred have been substantive posts, by any means. Added to this a small number of those posts were not written by me but by guest, who I was pleased to welcome to my humble Internet abode. However I have in fact posted a somewhat larger number of guest posts, of my own, at other blog sites scattered throughout the cyber-world.

However, putting aside all quibbles and mathematical niceties this is in fact the five hundredth post and it is normal on such occasions to pause and reflect, to take stock, to pass review on the evolution of those five hundred posts and I have decided to follow the convention by presenting for your contemplation ten of those five hundred posts for reconsideration.

I do not regard these as being in some way the ten best or my ten favourite posts. They are also not necessarily the ten most viewed posts, as, for reasons that I will explain in the coming summer, I do not look at my blog statistics. These posts are the ten posts that I think best reflect what I consider to be the principle aims of this blog. What this means in detail I shall explain in the introduction that I will now write to each of these ten posts.  For a more general description of those aims as I conceived them when I started this blog five hundred post ago I refer you to my second ever post: A Mission Statement.

The first of my ten is actually my third ever post and my first substantive history of science posting here at the Renaissance Mathematicus: A loser who was really a winner.

This is a post about the mostly sixteenth century Jesuit mathematician, astronomer and educational reformer Christoph Clavius (1538–1612). This post highlights the ahistorical practice of categorising scholars from the past as winners and losers e.g. Copernicus v Ptolemaeus or Darwin v Lamarck. All of the so-called losers made serious contributions to the evolution of science and deserve as much respect as the so-called winners. Secondly Clavius fulfils the important function on this blog of spotlighting the less well-known figures in the history of science to get away from the totally perverse concept of the big names and big events presentation of the history of science. Clavius also puts the lie to the widespread modern belief that religion, the Catholic Church and in particular the Jesuits were/are fundamentally anti-science. Lastly, I am a local historian of science and devote a fair amount of time to researching and making public the history of science of the area in which I live and work; Clavius is one of my locals.

Over the years on my blog I have gained something of a reputation for being down on Galileo Galilei. Although I have written a series of negative posts about Tuscany’s favourite son he’s not actually the real target of my complaints. What I object to is the hagiographical way in which leading figures in the history of science are presented by many writers. Lone scientific geniuses, ahead of their times, turning the world of science on its head with their brilliant ideas. This is without exception historically false and totally misrepresents how science actually develops and progresses. This type of hagiography is at its worst in the popular presentation of Galileo and I use him in my post Extracting the Stopper to illustrate just how many of the claims made for him concerning his uniqueness, believed to be true by the uninformed, are in fact historically false.

There is a strong tendency for people to think that scientific publications only consist of text, overseeing the illustrations. Since the dawn of printing illustration have played a central and highly significant role in scientific communication. In the post Where the pictures came from I took a look at all the various things that had to be developed in the Early Modern Period in order to make modern, printed, scientific illustrations possible.

The next post I’ve chosen to present here, Galileo’s great bluff…, might at first glance appear to be another attack on him, however the real aim of the post is another. Galileo and in modern times Thomas Kuhn, presented the transition from a geocentric world view to a heliocentric one, as a straight two way fight between Ptolemaeus in the red corner and Copernicus in the blue one with Galileo as a highly biased referee controlling the bout. As I outline in this post the story was a much, much more complex one with seven different astronomical systems involved in a cosmological Royal Rumble. This post illustrates the unfortunate tendency to over simplify the usually rather complex and messy evolution of science

Readers of this blog might just have noticed over the years that I tend to use both sarcasm and satire to mock those whom I believe to be committing history of science sins. I don’t try to force this but if my thoughts come out that way whilst I’m writing then I don’t suppress them either; in my opinion satire works best when it come spontaneously and naturally. The post The Empty Building, which emerged from my keyboard in twenty minutes of spontaneous writing, is a satire on those who believe that historically something only earns the name science if it is totally free of any suspicion of irrationality or illogical thought. The consequence of this definition of science is basically that there never has been any science.

My next choice is actually two related posts that take a look at two major myths concerning the emergence of heliocentric astronomy. The first, An Interesting Question, is what exactly the Catholic Church’s attitude towards science was in the early seventeenth century and how much influence their position had. The second connected myth, But it doesn’t move, is the common misconception that it was only religious prejudice that prevented the adoption of heliocentricity during this period, whereas the problem was actually a scientific one.

Many of the posts on this blog are in the form of potted biographies of important but not necessarily well-known figures in the history of science. The purpose of these post is to stimulate the reader to look beyond the usual litany of the so-called great: Galileo, Descartes, Newton, Darwin, Einstein etc., etc. Having set myself a limit of ten posts (although I’ve already cheated in the previous choice) for this retrospective I faced the difficult problem, which one or two (with Clavius in fact three) of these biographies to include here. In the end I settled on Hans Peter from Langendorf. The fierce competition for positions within the modern academic system is often reduced to the formula “publish or perish!” Any scientist is only as successful as the availability of his research results in published form, however often in the history of science very little thought is given to the scientific publishers who make it possible for the scholars to get their work into print. This post tells the story of the life and work of Johannes Petreius the Renaissance printer publisher who published, what is for many people the most important book in the history of science, Copernicus’ De revolutionibus. I chose him because I’m a local historian and he’s one of my locals. Any readers of this blog who come to visit me, and you are all very welcome to do so, get taken on my history of astronomy tour of Nürnberg, whether they want to or not. One of the high points of this tour is Petreius’ house where he printed De revolutionibus, in this post you get to see it without having to walk halfway through Nürnberg listening to me spouting on about Renaissance history.

This is followed by another of my potted biographies chosen for a very different reason. A fairly recent Internet review of my blog was pleasingly very positive but did call me to task because of the ratio of male to female scientists featured here, too biased to the male. In my own defence I would point out that I have tried to feature those, unfortunately few, women who have contributed to science in the period I mostly write about. Given this criticism this retrospective has to include at least one of those women. I have chosen Another Feminist Newtonian: Bologna’s Minerva a post about Laura Bassi the eighteenth century natural philosopher who became the first female professor at a European university and who as the title suggests was a strong supporter and propagator of the physics of Isaac Newton at a very early stage.

Over the years I have gained somewhat of a reputation for savage attacks on people who I believe are guilty of spreading of propagating inanity or total stupidity in the name of the history of science. This characteristic even led one notable digital historian to christen me The Hist-Sci Hulk! A persona that I adopted for a few weeks much to the annoyance of some of my readers. A retrospective would not be complete without one of the posts where I rip some offender a new one. I have chosen a pair of related posts in which I take on American pundit Adam Gopnik for his total misrepresentation of one of my favourite Renaissance figures, John Dee. I took apart and corrected Gopnik’s picture of Dee in the post A little learning is a dangerous thing and thought that would be the end of the matter. However Gopnik published a second piece a little later poring scorn on those who had dared to criticise his god like utterances concerning the magus. Thus I felt provoked to answer him again in the post, Help! I’ve been savaged by a toothless American bulldog. If you don’t like me being nasty then don’t read these two posts!

When I began to plan this post being well aware that my five hundredth posting was rapidly approaching I had intended to end it differently but circumstances intervened. Very early I made a decision to keep this blog largely single themed, the history of science in the widest sense. Other bloggers often cover a wide range of topics on their blogs, an approach I chose not to follow. However this is a blog and not an academic journal and I have from time to time included history of science related aspects of my private live amongst my posts, lectures I have held, visitors I have had and so on. Someone who has taken an active role in this personal aspect of the blog was my dog Sascha, who has been the public face of The Renaissance Mathematicus both here and on Twitter since the very beginning. This is not because I have chosen to remain anonymous, I have always blogged under my real name, but because I think he is much better looking than I. If you want to compare you can admire my visage here. However his contribution has over the years been much more than just lending his good looks to the blogs public image. He has from time to time featured in posts such as this one here and even hosted an edition of Giants’ Shoulders the history of science blog carnival. On a very personal level he was always present when I sat at the computer pecking out my posts letter for letter for your delectation, often lying at my feet waiting for me to finish so that I would feed him or go out for one of our walks. Regular readers will already know that Sascha left the building on the 23rd of December last year. Because of the constant support he gave me in writing this blog I’m dedicating this retrospective to his memory and closing it with the obituary that I wrote for him here, Sascha 16 August 2001 – 23 December 2013.

To write this post I didn’t rely on my memory in choosing the posts I have included but actually went through all four hundred and ninety-nine previous posts to make my selection. In doing so I was actually surprised at how many, in my opinion, posts I have written over the years that I would actually retain if I chose to delete all those that I don’t think are worth keeping. This insight has confirmed my resolve to keep on keeping on and I hope that at least some of you will stay with me for the next five hundred.

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Christmas Trilogy 2013 Part III: A New Year’s Offering.

Johannes Kepler wrote more than eighty books and pamphlets covering a wide range of mathematical and scientific topics. One of the most fascinating is the pamphlet he wrote as a New Year’s offering at the beginning of 1611. We’ll let Kepler introduce it for us:

The highly regarded Court Councillor of His Imperial Majesty, Herr Johannes Matthäus Wacker von Wackenfels, Golden Knight …, Supporter of the Sciences and Philosophy, my Gracious Benefactor.

Yes, I know that especial you love nothingness; however certainly not because of its slight value but rather much more because of the joyful and charming games, which one can, with lively jest, play with this word. It is easy for me to fancy that a present for you is all the more desirable and welcome the closer it approaches nothingness.

Wacker von Wackenfels Aegidius Sadeler

Wacker von Wackenfels
Aegidius Sadeler

Johannes Matthäus Wacker von Wackenfels (1550 – 1619) was lawyer, diplomat, humanist scholar and courtier, who having worked his way up the greasy pole of Renaissance absolutist court politics had, since 1597, been a member of one of the highest legal councils at the imperial court of Rudolph II, the Holy Roman German Emperor and Kepler’s employer. Wacker was an intelligent and well educated and widely read humanist scholar and Kepler’s closest friend at Rudolph’s court and the two Johanneses very much enjoyed chewing the intellectual cud with each other. It was Johannes Wacker, for example, who first brought Kepler the news of Galileo’s telescopic discoveries. It was good manners in those time for friends to give presents to each other at New Year and the pamphlet of which I have quoted the very flowery opening paragraphs was Kepler’s New Year’s offering to his friend Wacker in 1611.

This opening is followed by two pages of the various forms of nothingness that Kepler knows his friend to already possess. We then arrive at the core of Kepler’s offering to his friend:

As I went over the bridge deep in thought and full of worry and annoyed about my poverty, that is to come to you without a New Year’s offering, always following the same thoughts, to present this nothingness, or to find something that come closest to it, and exercised the astuteness of my thoughts on it, by chance the water vapour thickened through the cold to snow, and single small snowflakes fell on my coat, all were six-cornered with feathered spokes. Yes, by Heracles, that’s it, yes a phenomenon, smaller than a drop, and thereto of regular form. Yes, that is the wished for New Year’s offering for a friend of nothingness! Just as snow falls from the heavens and looks like the stars, so it is also suitable as the present of a mathematician who has nothing and receives nothing. Now quickly bring the present to my benefactor, as long as it exists and hasn’t through body warmth disappeared into nothingness.

Snowflake photo Alexey Kljatov  The Atlantic Dec 4 2013

Snowflake photo
Alexey Kljatov
The Atlantic Dec 4 2013

Here we have the subject of the pamphlet already expressed in its title, Strena seu de Nive sexangula, in English, New Year’s Offering or The Six-Cornered Snowflake. From here Kepler sets out to investigate the question, why are snowflakes six-cornered?

What follows is a rambling, at time fascinating, at others delightful discourse not just on six-cornered snowflakes but also the hexagonal cells of a honeycomb, the shape of pomegranate seeds, the arrangement of peas in a pod, the regular Platonic solids, the semi-regular Archimedean solids, three and six petaled flowers and various other things. Kepler discusses the tiling of planes and the filling of spaces. As one aspect of the latter he considers the best way to stack canon balls to occupy the least space. He had discussed this subject in his correspondence with Thomas Harriot who had been presented with this highly practical problem by his patron and employer, Sir Walter Raleigh. Kepler’s suggested solution, for which he could offer no proof, entered the history of mathematics as Kepler’s conjecture. Hilbert included it as problem eighteen in his famous list of twenty-three unsolved mathematical problems in 1900. The American mathematician Thomas Hales finally produced a generally accepted proof of Kepler’s conjecture that relies on a computer in 1998. Hales started on a more formal version of his proof, which he estimates will take twenty years, in 2003. Great oaks do truly from little acorns grow!

The Kepler conjecture makes The Six-Cornered Snowflake an important document in the history of mathematics. This is however not its only claim to scientific fame. Although comparatively primitive it is considered the first published scientific work in the discipline of crystallography.

But what of Kepler’s question, why is the snowflake six-cornered? In the end after all his considerations and diversions he is forced to admit defeat and acknowledge that he is unable to produce a satisfactory answer to his own question.

In the seventeenth century Kepler was not the only natural philosopher to consider the snowflake. René Descartes turned his attention to them in his Discourse on the Method

Sketch of snow crystal  René Descartes

Sketch of snow crystal
René Descartes

As did Robert Hooke in his microscopical investigations, which you can read about here.

Hooke's snowflakes

Hooke’s snowflakes

The first person to successfully photograph snowflakes was Wilson Alwyn “Snowflake” Bentley (February 9, 1865 – December 23, 1931).

Snowflakes Wilson Bentley

Snowflakes
Wilson Bentley

 

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The Renaissance Mathematicus Christmas Trilogy: An Explanation.

 

I seem to have garnered a number of new readers in the last twelve months who might be confused by my Christmas Trilogy especially as I have offered no explanation within the posts themselves, so I have decided to present a brief explanation of this Renaissance Mathematicus tradition.

Isaac Newton was born on 25th December 1642 (OS), Charles Babbage was born on 26th December 1791 and Johannes Kepler was born on 27th December 1571 (OS). These three are amongst my favourite figures in the history of science so I developed the habit of writing a post dedicated to some aspect of their life and work on their respective birthdays, hence The Renaissance Mathematicus Christmas Trilogy.

For those interested you can find links to previous years’ posts here:

2009: On Clocks and Triangles: a post for Newtonmas Is the question “who invented the computer” legitimate? Shedding some light.

2010: A Christmas Trinity I: Isaac was one too. A Christmas Trinity II: Charlie, Ivor, Robert and me. A Christmas Trinity III: Johann’s geometrical music.

2011: Only 26 and already a professor! How Charles tried to oust Isaac from Cambridge. Kepler contra Fludd, science contra woo?

2012:  Christmas Trilogy 2012 Part I: Did Isaac really victimise Stephen? Christmas Trilogy 2012 Part II: Charles and Ada: A tale of genius or exploitation? Christmas Trilogy 2012 Part III:  What to do if your mother’s a witch.

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Christmas Trilogy 2013 Part II: On Her Majesty’s Secret Service

From the modern standpoint Charles Babbage tends to be regarded as a one trick pony, “the father” of the computer. Now whilst it is true that Babbage’s obsession with his calculating engines played a very central role in much of his life, he actually applied his immense intelligence to a wide range of topics and projects. One of theses he seems to have regarded as a distraction as he tells us in his autobiography.

Deciphering is, in my opinion, one of the most fascinating of arts, and I fear I have wasted upon it more time than it deserves. I practised it in its simplest form when I was at school. The bigger boys made ciphers, but if I got hold of a few words, I usually found out the key. The consequence of this ingenuity was occasionally painful: the owners of the detected ciphers sometimes thrashed me, though the fault really lay in their own stupidity

Babbage was a cryptologist, and not just as a school boy, there is even some circumstantial evidence that like Alan Turing and John Wallis he served the powers that be as a code maker and breaker assisting Rear Admiral Sir Francis Beaufort, naval hydrographer and creator of the Beaufort Scale, during the Crimean War.

Babbage continued his schoolboy antics as an adult. He and his friend the physicist and inventor, Charles Wheatstone, took great pleasure in enciphering deciphering the coded messages in the classified advertisements in The Times. Wheatstone even going so far as send a new encoded message to a young lady, whose Oxford student friend had by this means proposed an elopement, telling her not to. In 1854 Babbage served as an expert witness in a law case. Enciphering Deciphering a letter sent by a Captain Childe to a mysterious lady. In the same year Babbage’s activities as a cryptologist reach a highpoint in an exchange of letters in the Journal of the Society of Arts concerning the so-called Vigenère cipher.

Named after Blaise de Vigenère by Bourbonnais, who had published it in his Traité de Chiffres in 1586 it was generally considered in the nineteenth century to be unbreakable. One of the most basic ciphers is the simple alphabetic substitution, named the Caesar cipher after Julius Caesar who is said to have used it, that most of us learn some time in primary school. In this cipher, each letter is replaced by a letter obtained by sliding one alphabet against another, e.g.

ABCDEFGHIJKLMNOPQRSTUVWXYZ

BCDEFGHIJKLMNOPQRSTUVWXYZA

Here Renaissance Mathematicus would become Sfobjttbodf Nbuifnbujdvt.

Such a cipher is naturally fairly easy to encipher and it is obvious that anybody wanting to indulge in serious coding would need something somewhat more complex, enter the Vigenère cipher, a polyalphabetic substitution cipher. In this each letter in the original message is fed through a different one of the 26 substitution alphabets according to a predetermined scheme. The cipher was given its final twist in that the alphabets used were chosen using a keyword known to both parties. I won’t go into details but for those interested you can find a good description in the Wikipedia article.

Before returning to Babbage it should be noted that although named after Vigenère this polyalphabetic cipher was not invented by him and we find quite a collection of significant Renaissance figures involved in its history.  The Renaissance polymath Leon Battista Alberti, who famously published the first account of linear perspective, wrote the earliest known account of the Vigenère cipher using a cipher disk in 1466, which was however first published posthumously in 1568. In a book written in 1508 but first published posthumously in 1518, the Renaissance occultist Johannes Trithemius independently discovered the Vigenère cipher in his case using a cipher tableau.  In 1553 Giovanni Battista Belaso published a pamphlet introducing the use of a key and in a work published in 1563 polymath and friend of Galileo, Giovanni Battista della Porto showed that the methods of Alberti and Trithemius were one and the same. Back to Babbage.

Over the centuries various people had (re)discovered the Vigenère cipher and in 1854 John Hall Brock Thwaites, a Bristol surgeon and dentist, claimed in a letter to the Journal of the Society of Arts to have invented an unbreakable cipher, which was in fact the keyword variation of the Vigenère cipher. This was pointed out to him in an anonymous letter from Babbage, who had almost certainly been consulted by the Society of Arts. Babbage closed his letter in his usual snide manner with the following remark:

“It may be laid down as a principle that it is never worth the trouble of trying any inscrutable cypher unless its author has himself deciphered some very difficult cypher”.

Stung by Babbage’s remark Thwaites challenged Babbage, given clear and encrypted message to supply the keywords used in the encryption. In his next letter Babbage obliged by doing just that revealing Thwaites’ keywords, two combined. He also returned the original message re-encrypted and challenged Thwaites in his turn to find his keywords, foreign supremacy. Thwaites withdrew from the unequal contest. This exchange of letters revealed Babbage to be a master cryptologist but didn’t reveal his working methods.

In fact Babbage had developed a general analytical method not only for the Vigenère cipher in question, but also for even more complex variations, using modulo arithmetic, which itself had only been first published by Gauss in 1801. Had Babbage published his results they would not only confirmed his high status as a mathematician but also established him as a leading cryptologists. In fact he did plan and make preparations for just such a publication, to be entitled The Philosophy of Deciphering, but never carried through on the project. Had he done so, his book would have been the first work of mathematical analysis in cryptology.

We now move onto the highly speculative part of this story. The mathematical method for breaking the Vigenère cipher was first published in 1863 by the German army officer Major Friedrich Wilhelm Kasiski, who received the credit for it, as a result of which the method is known as Kasiski analysis or Kasiski examination. This opens the question as to why Babbage didn’t claim credit for his discovery. Enter Beaufort.

Francis Beaufort is credited with having invented a cipher known as the Beaufort cipher that is in fact another variation of the Vigenère cipher. Now one of the puzzling facts is that there are no papers amongst Beaufort’s vast archives related to cryptology in general or the Beaufort cipher in particular, whereas a variation on the Beaufort cipher can be found amongst Babbage’s cryptology papers. Did Babbage in fact supply the Beaufort cipher and did the Admiralty, through Francis Beaufort, have access to Babbage’s methodology for solving Vigenère ciphers during the Crimean War giving them the same strategic advantage that the Allies enjoyed in terms of Enigma during the Second World War thanks to Bletchley Park? There are suggestions in Babbage’s papers and correspondence that this might indeed have been the case but no conclusive evidence. Was Babbage engaged on Her Majesty’s Secret Service as a code breaker? We will probably never know for certain but it’s nice to think that he was.

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Christmas Trilogy 2013 Part I: The Other Isaac [1].

In a recent post on John Wallis I commented on seventeenth century English mathematicians who have been largely lost to history, obscured by the vast shadow cast by Isaac Newton. One person, who has suffered this fate, possibly more than any other, was the first Lucasian Professor of Mathematics at Cambridge, and thus Newton’s predecessor on that chair, Isaac Barrow (1630 – 1677), who in popular history has been reduced to a mere footnote in the Newton mythology.

Statue of Isaac Barrow in the Chapel of Trinity College

Statue of Isaac Barrow in the Chapel of Trinity College

He was born in London in 1630 the son of John Barrow a draper. The Barrow’s were a Cambridge family notable for its many prominent scholars and theologians. Isaac father was the exception in that he had gone into trade but he was keen that his son should follow the family tradition and become a scholar.  With this aim in view the young Isaac was originally sent to Charterhouse School where he unfortunately more renowned as the school ruffian than for his learning. His father thus placed him in Felsted School in Essex, where John Wallis was also prepared for university, and where he soon turned his hand to more scholarly pursuits. Barrow’s success at school can be judged by the fact that when his father got into financial difficulties, and could no longer pay his school fees, the headmaster of the school took him out of the boarding house and lodged him in his own private dwelling free of charge and also arranged for him to earn money as tutor to William Fairfax.

In 1643 he was due to go up to Peterhouse Cambridge, where his uncle Isaac was a fellow. However his uncle was ejected from the college by the puritans and so the plan came to nought. Cut loose in society young Barrow ended up in Norfolk at the house of Edward Walpole a former schoolfellow who on going up to Cambridge decided to take Barrow with him and pay his keep. So it was that Barrow was admitted to Trinity College in 1646. Following further trials and tribulations he graduated BA in 1649 and was elected fellow shortly after. He went on to graduate MA in 1652 displaying thereby a mastery of the new philosophy. Barrow’s scholarly success was all the more remarkable, as throughout his studies he remained an outspoken Anglican High Church man and a devout royalist, things not likely to endear him to his puritan tutors.

In the 1650s Barrow devoted much of his time and efforts to the study of mathematics and the natural sciences together with a group of young scholars dedicated to these pursuits that included John Ray and Ray’s future patron Francis Willughby who had both shared the same Trinity tutor as Barrow, James Duport. Barrow embraced the mathematical and natural science of Descartes, whilst rejecting his metaphysics, as leading to atheism. He also believed students should continue to study Aristotle and the other ancients for the refinement of their language.  During this period Barrow began to study medicine, a common choice for those interested in the natural sciences, but remembering a promise made to himself whilst still at school to devote his life to the study of divinity he dropped his medical studies.

It was during this period that Barrow produced his first mathematical studies producing epitomes of both Euclid’s Elements and his Data, as well as of the known works of Archimedes, the first four books of Apollonius’ Conics and The Sphaerics of Theodosius. Barrow used the compact symbolism of William Oughtred to produce the abridged editions of these classical works of Greek mathematics. His Elements was published in 1656 and then again together with the Data in 1657. The other works were first published in the 1670s.

In 1654 a new wave of puritanism hit the English university and to avoid conflict Barrow applied for and obtained a travel scholarship leaving Cambridge in the direction of Paris in 1655. He spent eight months in Paris, which he described as, “devoid of its former renown and inferior to Cambridge!” From Paris he travelled to Florence where he was forced to extend his stay because an outbreak of the plague prevented him continuing on to Rome. In November 1656 he embarked on a ship to Smyrna, which on route was attacked by Barbary pirates, Barrow joining the crew in defending the ship acquitted himself honourably. He stayed in Smyrna for seven months before continuing to Constantinople. Although a skilled linguist fluent in eight languages Barrow made no attempt to learn Arabic, probably because of his religious prejudices against Islam, instead deepening his knowledge of Greek in order to study the church fathers.  Barrow left Constantinople in December 1658 arriving back in Cambridge, via Venice, Germany and the Netherlands, in September 1659.  It should be noted that the Interregnum was over and the Restoration of the monarchy would take place in the very near future. Unfortunately all of Barrow’s possessions including his paper from his travels were lost on the return journey, as his ship went up in flames shortly after docking in Venice

Barrow’s career, strongly supported by John Wilkins, now took off. In 1660 he was appointed Regius Professor of Greek at Cambridge followed in 1662 by his appointment as Gresham Professor of Geometry at Gresham College in London. His Gresham lectures were unfortunately lost without being published so we know little of what he taught there.  On the creation of the Lucasian Chair for Mathematics in 1663 Barrow was, at the suggestion of Wilkins, appointed as it first occupant. In 1664 he resigned both the Regius and the Gresham professorships. Meanwhile Barrow had started on the divinity trail being granted a BD in 1661 and beginning his career as a preacher.

Barrow only retained the Lucasian Chair for six years and in this time he lectured on mathematics, geometry and optics. His attitude to mathematics was strange and rather unique at the time. He was immensely knowledgeable of the new analytical mathematics possessing and having studied intently the works of Galileo, Cavalieri, Oughtred, Fermat, Descartes and many others however he did not follow them in reducing mathematics to algebra and analysis but went in the opposite directions reducing arithmetic to geometry and rejecting algebra completely. As a result his mathematical work was at one and the same time totally modern and up to date in its content whilst being totally old fashioned in its execution. Whereas his earlier Euclid remained a popular university textbook well into the eighteenth century his mathematical work as Lucasian professor fell by the wayside superseded by those who developed the new analysis. His optics lectures were a different matter. Although they were the last to be held they were the first to be published after he resigned the Lucasian chair. Pushed by that irrepressible mathematics communicator, John Collins, to publish his Lucasian Lectures Barrow prepared his optics lectures for publication assisted by his successor as Lucasian Professor, Isaac Newton, who was at the time delivering his own optics lectures, and who proof read and corrected the older Isaac’s manuscript. Building on the work of Kepler, Scheiner and Descartes Barrow’s Optics Lectures is the first work to deal mathematically with the position of the image in geometrical optics and as such remained highly influential well into the next century.

As he had once given up the study of medicine in his youth Barrow resigned the Lucasian Professorship in 1669 to devote his life to the study of divinity. His supporters, who now included an impressive list of influential bishops, were prepared to have him appointed to a bishopric but Barrow was a Cambridge man through and through and did not want to leave the college life. To solve the problem his friends had him appointed Master of Trinity instead, an appointment he retained until his tragically early death in 1677, just forty-seven years old. Following his death his collected sermons were published and it is they, rather than his mathematical work, that remain his intellectual legacy. Throughout his life all who came into contact with him acknowledge Barrow as a great scholar.

Near the beginning of this post I described Barrow as, having “been reduced to a mere footnote in the Newton mythology”. What did I mean by this statement and what exactly was the connection between the two Isaacs, apart from Barrow’s Optics Lectures? Older biographies of Newton and unfortunately much modern popular work state that Barrow was Newton’s teacher at Cambridge and that the older Isaac in realising the younger Isaac’s vast superiority as a mathematician resigned the Lucasian Chair in his favour. Both statements are myths. We don’t actually know who Newton’s tutor was but we can say with certainty that it was not Barrow. As far as can be ascertained the older Isaac first became aware of his younger colleague after Newton had graduated MA and been elected a fellow of Trinity. The two mathematicians enjoyed cordial relations with the older doing his best to support and further the career of the younger. As we have already seen above Barrow resigned the Lucasian Professorship in order to devote his live to the study and practice of divinity, however he did recommend his young colleague as his successor and Newton was duly elected to the post in 1669. Barrow also actively helped Newton in obtaining a special dispensation from King Charles, whose royal chaplain he had become, permitting him not to have to be ordained in order to hold the post of Lucasian Professor[2].


[1] On Monday I wrote that I might not be blogging for a while following Sascha untimely death. However I spent some time and effort preparing this years usual Christmas Trilogy of post and I find that writing helps to divert my attention from thoughts of him and to stop me staring at the wall. Also it’s what Sascha as general manager of this blog would have wanted.

[2] Should anyone feel a desire to learn more about Isaac Barrow I can highly recommend Before Newton: The Life and Times of Isaac Barrow, ed. Mordechai Feingold, CUP, Cambridge, 1990 from which most of the content of this post was distilled.

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